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Title: The braid and the Shi arrangements and the Pak–Stanley labelling
Author: Duarte, Rui
Guedes de Oliveira, António
Keywords: Parking functions
Shi arrangement
Braid arrangement
Issue Date: Nov-2015
Publisher: Elsevier
Abstract: In this article we study a construction, due to Pak and Stanley, with which every region RR of the Shi arrangement is (bijectively) labelled with a parking function λ(R). In particular, we construct an algorithm that returns R out of λ(R). This is done by relating λ to another bijection, that labels every region S of the braid arrangement with r(S), the unique central parking function f such that λ−1(f)⊆S. We also prove that λ maps the bounded regions of the Shi arrangement bijectively onto the prime parking functions. Finally, we introduce a variant (that we call “s-parking”) of the parking algorithm that is in the very origin of the term “parking function”. S-parking may be efficiently used in the context of our new algorithm, but we show that in some (well defined) cases it may even replace it.
Peer review: yes
DOI: 10.1016/j.ejc.2015.03.017
ISSN: 1095-9971
Appears in Collections:CIDMA - Artigos
AGG - Artigos

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